一类Caputo分数阶微分方程多点边值问题的多解性

本文讨论了一类Caputo分数阶微分方程多点边值问题的多解性,通过把分数阶微分方程的边值问题转化成与其等价的积分方程问题求出边值问题的Green函数并得到其格林函数的相关性质,最后利用锥上不动点指数定理研究分数阶微分方程多点边值问题正解和多个正解的存在性.     

一类分数阶微分方程m点边值问题正解的存在性

给出了一类分数阶微分方程m点边值问题的格林函数,通过讨论其性质,运用uo有界算子和不动点指数理论,在与相应的线性算子第一特征值有关的条件下获得了分数阶微分方程多点边值问题正解及多个正解的存在性结果.     

分数阶微分方程多点分数阶边值问题

研究分数阶微分方程多点分数阶边值问题解的存在性与唯一性,利用不动点定理,得到了边值问题存在唯一解和至少存在1个解的充分条件.     

Hilfer-Katugampola序列分数阶微分方程边值问题Lyapunov型不等式

研究了Hilfer-Katugampola序列分数阶微分方程多点边值问题Lyapunov型不等式.首先,利用Hilfer-Katugampola分数阶微积分的定义和性质将HilferKatugampola序列分数阶微分方程边值问题等价转化为带有Green函数的积分方程问题.其次,定义相应的Banach空间并结合先验估计方法得到了Lyapunov型不等式.最后,通过给出一系列推论说明该文研究结果推广和丰富了已有文献相关工作.     

非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性

本文研究一类非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性,利用一些标准的不动点定理进行证明.     

一类分数阶差分方程多解的存在性

利用基本的不动点定理研究了一类分数阶q-差分方程多点边值问题.得到了边值问题多解的存在性,并给出了具体的实例来验证文中的结论.     

一类分数阶微分方程奇异多点边值问题解的存在性和唯一性

研究一类非线性分数阶微分方程奇异多点边值问题,利用Schauder不动点定理以及压缩映像原理,得到了边值问题解的存在性及唯一性的充分条件.     

一类含p-Laplacian算子的分数阶时滞微分方程无穷多点边值问题的正解

主要研究一类含有p-Laplacian算子和时滞的分数阶微分方程的无穷多点边值问题.先构造Green函数并分析其性质,再利用p-Laplacian算子的性质和Banach压缩映射原理,得到这类边值问题正解存在唯一的一些新结果.     

一类分数阶微分方程多点边值问题正解的存在性

本文研究一类分数阶微分方程的多点边值问题.利用Guo-krasnoselskii不动点定理和Leggett-Williams不动点定理,得到正解的存在性和多重性结果.通过一个简单的例子说明了主要结果的应用.     

非线性分数阶微分方程三点边值问题解的存在性

讨论了一类非线性分数阶微分方程三点边值问题解的存在性.微分算子是Riemann-Liouville导算子并且非线性项依赖于低阶分数阶导数.通过将所考虑的问题转化为等价的Fredholm型积分方程,利用Schauder不动点定理获得该三点边值问题至少存在一个解.     

二阶常微分方程无穷多点边值问题的正解

该文运用锥上的不动点定理研究非线性二阶常微分方程无穷多点边值问题 u'+a (t ) f (u)=0, t∈(0, 1), u(0)=0, u(1)=∑^∞_{i =1}α _i u ( ξ _i ) 正解的存在性. 其中ξ _i∈ (0,1),α _i∈ [0,∞), 且满足∑^∞_i=1α_iξ _i <1.α∈C([0,1], [0,)),f∈C ([0,∞), [0,∞)).     

GLOBAL EXISTENCE OF THE SOLUTION OF NONLINEAR SCHRDINGER EQUATIONS IN EXTERIOR DOMAINS

In this paper,we discuss the problem for the nonlinear Schr(?)dinger equation(?)where Ω is the exterior domain of a compact set in B~n,a_j(u)=O(|u|),b_j(u)=O(|u|)(1≤j≤n),c(u)=O(|u|~2)near u=0.If n≥5,some Sobolev norm of u_0(x)is sufficiently small,under suitableassumptions on smoothnessand and compatibility and the shape of Ω,we get that the problem has aunique global solution u(t,x),with the decay estimate‖u(t,·)‖_(L(?)(Ω))=O(t~(-n/4)),‖u(t,·)‖_(L~4(Ω))=O(t~(-n/4)),t→+∞.     

On the blow-up of solutions to anisotropic parabolic equations with variable nonlinearity

The aim of this paper is to establish sufficient conditions of the finite time blow-up in solutions of the homogeneous Dirichlet problem for the anisotropic parabolic equations with variable nonlinearity $ u_t = \sum\nolimits_{i = 1}^n {D_i (a_i (x,t)|D_i u|^{p^i (x) - 2} D_i u) + \sum\nolimits_{i = 1}^K {b_i (x,t)|u|^{\sigma _i (x,t) - 2} u} } $ u_t = \sum\nolimits_{i = 1}^n {D_i (a_i (x,t)|D_i u|^{p^i (x) - 2} D_i u) + \sum\nolimits_{i = 1}^K {b_i (x,t)|u|^{\sigma _i (x,t) - 2} u} } . Two different cases are studied. In the first case a _i ≡ a _i (x), p _i ≡ 2, σ _i ≡ σ _i (x, t), and b _i (x, t) ≥ 0. We show that in this case every solution corresponding to a “large” initial function blows up in finite time if there exists at least one j for which min σ _j (x, t) > 2 and either b _j > 0, or b _j (x, t) ≥ 0 and Σ_π b _j ^−ρ(t)(x, t) dx < ∞ with some σ(t) > 0 depending on σ _j . In the case of the quasilinear equation with the exponents p _i and σ _i depending only on x, we show that the solutions may blow up if min σ _i ≥ max p _i , b _i ≥ 0, and there exists at least one j for which min σ _j > max p _j and b _j > 0. We extend these results to a semilinear equation with nonlocal forcing terms and quasilinear equations which combine the absorption (b _i ≤ 0) and reaction terms.     

半线性中立型分数阶微分方程S-渐近ω周期解

在Banach空间X中,研究了如下半线性Caputo-分数阶中立型微分方程S-渐近w周期解的存在性其中0α1,-A是解析半群{T(t)}_(t≥0)的无穷小生成元.     

Problem of the extremal decomposition of a closed plane

One considers the problem of the maximum of the product of powers of conformal radii of nonoverlapping domains in the following formulation. Let A=a₁, ..., a_n and B=(b₁, ..., b_m be systems of distinguished points in ¯C and let ={₁,..., _m} be a system of positive numbers. ByU(D,b ) we denote the reduced modulus of the simply connected domain D relative to the pointb D. Find the maximum of the sum in the familyD of all systems of nonoverlapping simply connected domains D_j, j=1, ..., m, satisfying the following condition: the domain D_j does not contain points b_i B, different from b_j, and some collection A_j, for each domain, of points from A, _j=1 ^m A _j =A. The solution of this problem is obtained by the simultaneous use of the method of variation and of the method of the moduli of families of curves and is given by Theorem 1 of the present paper. As consequences of Theorem 1 one obtains Theorems 2 and 3, strengthening the corresponding results of a previous paper of the author.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 149–154, 1985.     

一类弱奇异边值问题的大范围收敛算法

该文研究如下的弱奇异边值问题: (p(x)y')'=f(x, y),0b₀g(x), 0≤b₀<1, 边值条件为y(0)=A,αy(1)+β y'(1)=γ 或y'(0)=0,αy(1)+βy'(1)=γ (R.K.Pandey 和 Arvind K.Singh 给出了一种求解此问题的二阶有限差分方法^[1]. 在再生核空间中讨论方程解的存在性, 给出一种新的迭代算法,这种迭代算法是大范围收敛的. 给出数值算例并与R. K. Pandey 和Arvind K.Singh 给出的方法进行比较说明该文方法的有效性.     

Positive Solution of Multi-Point Boundary Value Problems for the One-Dimensional p-Laplacian with Singularities

In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{（ φp（u＇））＇＋q（t）f（t,u,u＇）=0,0〈t〈1,u（0）=∑i=1^nαiu（ξi）,u＇（1）=∑i=1^nβiu＇（ξi）,whereφp（s）=｜s｜^p-2s,p≥2;ξi∈（0,1）（i=1,2,…,n）,0≤αi,βi〈1（i=1,2,…n）,0≤∑i=1^nαi,∑i=1^nβi〈1,and q（t） may be singular at t=0,1,f（t,u,u＇）may be singular at u＇=0     

Sums of almost equal prime cubes

We prove that almost all integers N satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 5; 6; 7; 8, i.e., N = p ₁³ + ... + p _j ³ with |p _i − (N/j)^1/3| ≦ $ N^{1/3 - \delta _j + \varepsilon } $ N^{1/3 - \delta _j + \varepsilon } (1 ≦ i ≦ j), for δ _j = 1/45; 1/30; 1/25; 2/45, respectively.     

Score sets in oriented 3-partite graphs

Let D(U, V, W) be an oriented 3-partite graph with |U|=p, |V|=q and |W|= r. For any vertex x in D(U, V, W), let d x and d-x be the outdegree and indegree of x respectively. Define aui (or simply ai) = q r d ui - d-ui, bvj(or simply bj) = p r d vj - d-vj and Cwk (or simply ck) = p q d wk - d-wk as the scores of ui in U, vj in V and wk in Wrespectively. The set A of distinct scores of the vertices of D(U, V, W) is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai(2≤i≤n - 1) are even positive integers and an is any positive integer, then for n≥3, there exists an oriented 3-partite graph with the score set A = {a1,2∑i=1 ai,…,n∑i=1 ai}, except when A = {0,2,3}. Some more results for score sets in oriented 3-partite graphs are obtained.     

Higher integrability for minimizers of variational integrals with nonstandard growth

We consider a (possibly) vector-valued function u: Ω→R ^N, Ω⊂R ⁿ, minimizing the integral , whereD _iu=∂u/∂x _i, or some more general functional retaining the same behaviour; we prove higher integrability forDu:D ₁u,…,D_n−1u∈L^q, under suitable assumptions ona _i(x).

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Sunto Consideriamo una funzione u: Ω→R ^N, Ω⊂R ⁿ che minimizzi l'integrale , doveD _iu=∂u/∂x_i, o un funzionale con un comportamento simile; sotto opportune ipotesi sua _i(x), dimostriamo la seguente maggiore integrabilità perDu:D ₁u,…,D_n−1uεL^q.